How to Calculate Percentages (and the Two Traps Everyone Falls Into)

Three formulas cover nearly every percentage question. Two traps catch nearly everyone. And 23.6% of simple whole-number percentage sums come out with a binary leftover in JavaScript.

The Three Questions

Almost every percentage question is one of three shapes. A percentage of a number: 15% of 80 is 15 / 100 × 80 = 12. One number as a percentage of another: 18 out of 24 is 18 / 24 × 100 = 75%. Percentage change: from 80 to 100 is (100 − 80) / 80 × 100 = a 25% increase. The rest are rearrangements: increasing 50 by 20% is 50 × 1.2 = 60, and if 30 is 15% of something, the whole is 30 / 0.15 = 200. Our Percentage Calculator answers all of them and shows the working.

Trap 1: Changes Don’t Cancel

A 20% rise followed by a 20% fall does not get you back where you started: 100 → 120 → 96, a 4% loss overall. The fall is 20% of the bigger number. The same asymmetry shows up between directions: from 80 to 100 is a 25% increase, but from 100 to 80 is a 20% decrease. Always ask “percent of what?”; the starting value is the base.

Trap 2: Percent vs Percentage Points

When a rate changes, there are two ways to describe it. An interest rate going from 4% to 5% has risen by 1 percentage point, which is a 25% increase in the rate. Both are true, and mixing them up makes a change sound four times bigger or smaller than it is. Use percentage points for the difference between two percentages, and percent for relative change.

Why Calculators Sometimes Show 7.000000000000001

Computers store numbers in binary, where most decimals cannot be written exactly, so arithmetic leaves tiny leftovers. In JavaScript, 7 / 100 × 100 is 7.000000000000001. We counted how often it happens in everyday questions: 8 of the 101 questions “X% of 100” with X from 0 to 100, and 2,361 of 10,000 (23.6%) of all “X% of Y” questions with whole numbers from 1 to 100. Our calculator rounds results to 10 significant digits for display, which removes the leftovers without hiding genuine decimals like the 33.33333333 in one third.

Percentages, Fractions and Exact Answers

A percentage is a fraction over 100, and the cleanest way to avoid rounding trouble is to stay in fractions as long as you can. One third plus one sixth is exactly one half; done in decimals it can come out as 0.4999999. Every fraction’s decimal either ends (3/8 = 0.375) or repeats forever (1/7 = 0.142857 with those six digits repeating). Our Fraction Calculator keeps numerators and denominators as exact whole numbers, shows the steps, and marks the repeating digits with a bar; it matched Python’s exact fractions on 3,000 random problems.

Order of Operations on a Calculator

Percentages often sit inside longer sums, and calculators disagree about how to read them. The standard order is brackets, then powers, then multiplication and division from left to right, then addition and subtraction, and the minus sign in front of a number comes after powers, so -2^2 is -4, not 4. Typing 1/2pi means (1/2) × π; for 1/(2π) use brackets. Our Scientific Calculator follows exactly these rules with its own parser, and agreed with Python’s math library on 3,000 random expressions.

Frequently Asked Questions

Published Oct 14, 2026 by Derek Giordano